An AB Initio Calculation of the Pd-V FCC Superstructure Phase Diagram with Fourth Nearest Neighbor Cluster Interactions
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AN AB INITIO CALCULATION OF THE Pd-V FCC SUPERSTRUCTURE PHASE DIEAGRAM WITH FOURTH NEAREST NEIGHBOR CLUSTER INTERACTIONS
PATRICK D. TEPESCH*, G. CEDER*, C. WOLVERTON"', D. DE FONTAINE** *Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA *'University of California-Berkeley, Berkeley, CA.
ABSTRACT The Monte Carlo technique was used to calculate the phase diagram of the fcc superstructures in the Pd-V system using up to fourth nearest neighbor, concentration independent, pair and multiplet interactions. The interactions were computed by the method of Direct Configurational Averaging using a Linearized Muffin-Tin Orbital Hamiltonian cast into the tight binding form. The phase diagram was computed with a fast Monte Carlo simulation technique using environment sampling. The two fcc ground states in experimental diagram are predicted to be stable. The computed transition temperatures are higher than those found experimentally. I.
INTRODUCTION
With the increase in computing power over the past decade, the first principles calculation of phase diagrams has become feasible. One model which has been used successfully for this purpose is the alloy-Ising model [1]. There is an exact transformation between the energy as computed from quantum mechanical methods and the Hamiltonian of the Ising model. The fcc superstructure phase diagram of the Pd-V system is computed within this framework. The process of computing the phase diagram can be broken down into three basic steps. First, the coefficients in the Ising expansion of the energy are computed from quantum mechanical methods. Second, the ground states of the system are determined. Finally, the temperature-composition phase diagram is computed. H. CALCULATION OF THE EFFECTIVE CLUSTER INTERACTIONS A. An Ising-like expansion for the Energy In the alloy-Ising model the energy of the alloy is expanded as a function of configuration on a particular lattice in terms of cluster functions. In its most general form the expansion is written [1]: H( {o} ) = 5 V~jo 1 ( {(}a),
(1)
where {I} is the configuration on the lattice, Vo, is the effective cluster interaction (ECI) for the cluster a, and act is the product of all spins on cluster a. Spin +1(-1) on a site of the lattice represents the presence of an A(B) atom . The summation in equation (1), in principle, goes over all clusters on the lattice. Since the cluster functions, oa, form a complete and orthogonal set of basis functions [2], the expansion is exact and the effective cluster interactions, Va, are uniquely defined as the coefficients of this expansion. Mat. Res. Soc. Symp. Proc. Vol. 291. Q1993 Materials Research Society
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B. Effective Cluster Interactions for the fcc Pd-V system The effective cluster interactions (ECI) for the Pd-V system were calculated by Direct Configurational Averaging (DCA) using an LMTO Hamiltonian cast into the tight binding form [3]. For the Pd-V system, 26 ECI's were calculated including 1st through 401 and 6th nearest neighbor pairs, 14 triplets, and 8 quadruple
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